中高孔隙率泡沫金属材料常数的细观统计特性与拉伸本构关系

Meso statistics properties of material constants and constitutive relation of medium or high void ratio metal foams under tension

Gibson-Ashby单元模型成功地用于高孔隙率的开孔泡沫金属材料的弹性模量和屈服应力的预测,但基于该模型的破坏强度(应变)公式尚未建立,而在拉伸等条件下,泡沫金属的细观结构破坏对材料性质产生重大影响.本文重点研究在拉伸条件下Gibson-Ashby单元的破坏模式,通过综合考虑单元内水平梁的弯曲和立柱拉伸综合效应,建立起更一般性的泡沫金属材料单元的弹性模量、屈服应力(应变)公式.并且应用塑性铰长度的概念,成功地推导出单元的破坏应变.进而用单元结构几何参数的概率分布来表征泡沫金属的细观非均匀性,从而分别推导出了开孔泡沫金属单元材料参数的概率分布函数,并以此建立了涵盖支持中、高孔隙率泡沫金属的拉伸本构关系.通过对单元弹性模量、屈服应变与破坏应变的概率分布分析,指出它们的概率分布均存在近似的但不相互独立的等效Weibull分布,这说明在研究材料常数的细观统计特性时,有必要考虑材料的细观变形和破坏特性.

The Gibson-Ashby＇s cubic cell model had been successfully used to predict the elastic modulus and （the） yield stress of high void ratio open-cell foams, but the cells failure behavior was unknown yet in the model.The failure of metal foam＇s meso cell would take great important roles on their material properties in tension.This paper focused on the failure mode of Gibson-Ashby cell under tension, by considering the combining effects of the beam＇s bending and column＇s stretching in the cell, the more general formulas about the cell＇s elastic modulus, yield stress （strain） were established.Further, by applying the concept of the length of plastic hinge, the failure strain of the cell was deduced successfully.The theoretical results were verified by the 3D FEM analysis of the cell.Further, we use the probability distribution of cell geometry parameter to reflect the heterogeneous meso-structure of metal foam, and based on the statistical method, the probability distributions of material parameters of cells and the constitutive relation of metal foam with medium or high void ratio were deduced.The analysis of probability distributions of the elastic modulus, yield strain and failure strain shows that these probability distributions can be substituted by equivalent but not independent Weibull distribution respectively.It is show that when we study on the meso probability of materials, the deformation and failure properties should be considered carefully.